1. Field of the Invention
The present invention relates generally to an image forming apparatus, such as a printer, a facsimile machine or a copying machine, which outputs printed images formed by using toner. More particularly, the invention is concerned with an image forming apparatus featuring a gamma characteristic correction function for optimizing toner density output values, for instance, according to input gradations (tone levels), as well as a storage medium storing a gamma correction program used for making gamma correction and a method of gamma correction.
2. Description of the Related Art
Conventionally, an image forming apparatus like a printer generates an image signal from input print data by performing image forming operation, adjusts toner densities according to the image signal and, then, produces and delivers a printout carrying an image printed with proper gradations. This kind of image forming apparatus is configured to carry out so-called gamma correction to correct a gamma characteristic of the apparatus so that toner densities on each printout match the image signal. Ideally, the gamma characteristic should be such that the toner density linearly increases with an increase in gradation. Practically, however, individual image forming apparatuses have varying gamma characteristics and, thus, each image forming apparatus is subjected to a gamma correction process and thereby initialized to provide a linear gamma characteristic at a final stage of manufacture.
Although each image forming apparatus is properly initialized to provide a linear gamma characteristic as mentioned above, the gamma characteristic of each apparatus deviates from an initial setting thereof, causing irregularities in the density of toner adhering to a photosensitive member, due to changes that occur with the lapse of time. For this reason, a conventional image forming apparatus is re-subjected to the gamma correction process at regular time intervals or when the amount of deviation of the gamma characteristic of the apparatus from the initially set linear gamma characteristic exceeds a threshold value, for example, so that toner densities on each printout become normal.
Generally, the gamma correction process carried out by the conventional image forming apparatus includes the steps of causing toner particles to adhere to the photosensitive member according to patch images used for gamma correction, measuring toner densities of the patch images by a sensor, and correcting the gamma characteristic of the apparatus based on measured values of the toner densities. The patch images taken from a test print as samples usually contain not a little noise components, so that it is necessary to repeatedly measure the toner densities of the patch images several times or increase the number of sampled patch images and, then, calculate mean values of measured data in order to reduce the influence of noise.
However, if the toner densities of the patch images are repeatedly measured or the number of sampled patch images is increased, the gamma correction process would require extra processing time for generating the patch images and measuring the toner densities thereof, resulting in a reduction in overall processing speed.
One approach conventionally used to cope with the aforementioned problem is to measure toner densities of patch images taken at a predetermined small number of sample points (e.g., 8 sample points) of gradation and interpolate measured values of the toner densities a multiple number of times to increase the number of samples in order to obtain samples of substantially continuous gradations to determine the entire gamma characteristic.
Specifically, if it is intended to determine the gamma characteristic from 8 sample points as shown in FIG. 14, the aforementioned gamma correction approach employs a method of interpolating operation performed on four consecutive sample points, for example. In the example of FIG. 14, formulae of straight lines L1, L2, L3 containing line segments S1S2, S2S3, S3S4 are determined and Y values (density values) N1, N2, N3 on the respective line segments S1S2, S2S3, S3S4 at a gradation value x1 on an x-axis are calculated.
Then, the aforementioned density values N1, N2, N3 are weighted and an interpolation point of the weighted density values N1, N2, N3 is obtained. In this process, the interpolation point is calculated each time by weighted averaging operation performed by using a predefined equation (α·N1+β·N2+γ·N3) based on a predetermined weight ratio {α, β, γ}, or based on a ratio of distances between points of the individual density values N1, N2, N3, for example.
If the interpolating operation of the aforementioned interpolation method of the prior art is used to interpolate sample points S0-S7 which are located as shown in FIG. 13, for example, an interpolation point X1 in a region S1-S2 is obtained by determining a point N1 on a straight line containing a line segment S0S1, a point N2 on a straight line containing a line segment S1S2 and a point N3 on a straight line containing a line segment S2S3 at the same x-coordinate as a midpoint of the line segment S1S2 and calculating a mean value of lightness values of the points N1, N2, N3. In this example, the point N3 is located significantly apart from the point N2 and, for this reason, the interpolation point X1 deviates from a true gradation characteristic curve. A similar situation occurs with an interpolation point X6 obtained for a region S6-S7 as well.